Can anyone explain this problem with an aid of a diagram?

Question

Leo Abeyta · Accepted Answer

The resultant force is 86.74 N at an angle of 72.1°

Sorry, no diagram!

First, you will resolve each vector (given here in standard form) into rectangular components (#x# and #y#). Then, you will add together the #x-#components and add together the #y-#components. This will given you the answer you seek, but in rectangular form. Finally, convert the resultant into standard form. Here's how: Resolve into rectangular components (note the changes of angle measure into standard angles): #Fx_1 = 35 cos 110° = 35 (-0.342) = -11.97 N# #Fy_1 = 35 sin 110° = 35 (0.940) = 32.89 N# #Fx_2 = 60 cos 90° = 0 N# #Fx_1 = 60 sin 90° = 60 N# #Fx_3 = 40 cos -15° = 40 (0.969) = 38.64 N# #Fy_3 = 40 sin -15° = 40 (-0.259) = -10.35 N# Now, add the one-dimensional components #F_x = F_(x1)+F_(x2) +F_(x3) = 26.67 N# and #F_y = F_(y1)+F_(y2) +F_(y3) = 82.54 N# This is the resultant force in rectangular form. With a positive #x#-component and a positive #y#-component, this vector points into the 1st quadrant. Now, convert to standard form: #F = sqrt((F_x)^2+(F_y)^2) = sqrt((26.67)^2+82.54^2) = 86.74 N# #theta=tan^(-1)(82.54/(26.67)) = 72.1°#

Charlotte Aaron · Answer

#"Problem was solved again."#

#"all forces acting on object"#

#".................................................................................................."#

#"The Force "F_1" and its components(vertical,horizontal)"#

#F_("1x")=-F_1.sin(20)=-35.0,34202014=-11.97" N"#

#F_("1y")=F_1.cos(20)=35.0,93969262=32.89" N"#

#"...................................................................................."#

#"The Force "F_2" and its components(vertical,horizontal)"#

#"The Force "F_2 " has vertical component only ."#

#F_("2x")=0#

#F_("2y")=60" N"#

#"...................................................................................................."#

#"The Force "F_3" and its components(vertical,horizontal)"#

#F_("3x")=F_3.sin(75)=40.0,96592583=38.64" N "#

#F_("3y")=-F_3.cos(75)=-40.0,25881905=-10.35" N"#

#.....................................................................................................#

#"now let us find the total "F_x" and "F_ y " components."#

#F_x=F_("1x")+F_("2x")+F_("3x")#

#F_y=F_("1y")+F_("2y")+F_("3y")#

#F_x=-11.97+0+38.64=26.67" N"#

#F_y=32.89+60-10.35=82.54" N"#

#".................................................................................."#

#"Resultant Vector..."#

#" magnitude of the resultant vector can be calculated :"#

#F=sqrt((F_x)^2+(F_y)^2)#

#F=sqrt((26.67)^2+(82.54)^2)#

#F=sqrt(711.2889+6812.8516)#

#F=sqrt(7524.1405)#

#F=86.74" N"#

#"we must find " tan(theta) " for direction of the resultant vector."#

#tan(theta)=(F_x)/(F_y)#

#tan(theta)=(26.67)/(82.54)#

#tan(theta)=0.32311606#

#theta=17.91 #

Nora Arzate · Answer

undefined Certainly! This problem involves calculating the force between two point charges located at specific coordinates in three-dimensional space. The force between the charges can be determined using Coulomb's law, which states that the force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

To illustrate the problem with a diagram, we can represent the two charges (-1 C and 4 C) as points in three-dimensional space. The first charge, -1 C, is located at the point (-2, 6, -8), and the second charge, 4 C, is located at the point (2, -4, 1).

Using these coordinates, we can draw a three-dimensional coordinate system with axes labeled x, y, and z. Then, we can plot the two points corresponding to the positions of the charges. The point (-2, 6, -8) represents the location of the -1 C charge, and the point (2, -4, 1) represents the location of the 4 C charge.

Once the points are plotted, we can draw a line segment connecting the two points to represent the distance between them. This line segment will serve as the vector along which the force acts.

To calculate the force between the charges, we use Coulomb's law, which involves the magnitudes of the charges, the distance between them, and a constant. With the charges given in the problem (-1 C and 4 C), and knowing the coordinates of the points, we can plug these values into Coulomb's law to find the magnitude and direction of the force vector.

Finally, we can represent the force vector on the diagram by drawing an arrow along the line segment connecting the two charges. The direction of the arrow indicates the direction of the force, and the length of the arrow represents the magnitude of the force.

Overall, the diagram helps visualize the problem and understand how the forces between the charges are calculated based on their positions in three-dimensional space.